Addressing Non-linear Hardware Limitations and Extending Network Coverage Area for Power Aware Wireless Sensor Networks

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Addressing Non-linear Hardware Limitations and Extending Network

Coverage Area for Power Aware Wireless Sensor Networks

Michael Walsh and Martin Hayes

1 Addressing Non-linear Hardware Limitations

and Extending Network Coverage Area for

Power Aware Wireless Sensor Networks

Michael Walsh

1

and Martin Hayes

2

1_{CLARITY: Centre for Sensor Web Technologies}

Tyndall National Institute,

University College Cork,

Cork, Ireland,

2

_{University of Limerick}

Limerick, Ireland

1. Introduction

Heterogeneous Wireless Sensor Network (WSN) technology will soon emerge from the research laboratories around the world and become embedded in everyday life. Here it will actuate, sample and organize at a scale previously thought impossible. WSNs offer an alternative to the wired communications network or can be deployed rapidly in a previously un-serviced area where they provide the ability to observe physical phenomena at a fine resolution over large spatio-temporal scales.

A wireless sensor is in essence a miniature computer which can be placed anywhere or attached to anything. Typically it is powered by a battery that should be small and ideally need replacement as infrequently as possible. These ubiquitous or pervasive devices are typically in-expensive, miniature, and capable of independent computation, communication and sensing. Continuing improvements in affordable and efficient integrated electronics is having a considerable impact on the technology, that can underpin the sensor network itself and to that end, a number of state of the art sensor node platforms are now readily available. The WSN can be viewed in two ways, firstly as a decentralised group of wireless sensor nodes each limited in terms of memory, computation and functionality. Alternatively and as is more commonly the case, a WSN can be viewed as the sum of its parts. The addition of nodes to a network therefore increases the overall capabilities of the network, while the distributed manner in which these nodes are added allows the network to retain its ability to self-heal and organise.

The application space for WSNs is quite large and continues to expand vigorously encompassing habitat, ecosystem, seismic and industrial process monitoring, security and surveillance as well as rapid emergency response and wellness maintenance. This unsurprisingly has generated significant attention within the research community where the question of performance robustness and optimisation appears to be a recurring theme. The

(3)

engineer is therefore presented with many challenges when designing an effective deployment.

2. Wireless Sensor Network Challenges

There are numerous challenges that must be addressed when designing a WSN. There follows a brief look at a number of problems, general in the wireless context, to which systems science can provide a useful solution.

2.1Reliable Quality of Service

In a survey carried out amongst possible users of industrial wireless technology (IMS Research, 2006), 43% of the surveyed suggested that communications reliability was a major barrier to the uptake of wireless solutions in industry. The provision for Quality of Service (QoS) is therefore a key requirement if any form of WSN market penetration is to be generated. QoS has a number of different associated meanings (Goldsmith, 2006; Rappaport, 2002). In this work, QoS is taken, where specified, to imply one or both of the following

1. QoS implies that the transmitted signal will exhibit certain minimum signal strength at the receiver. This in turn will guarantee pre-specified levels of Bit Error Rate (BER) and improve demodulation at the point of access.

2. System connectivity must be ensured under the assumption that the communication link will be severed if some reliable measurable link quality metric falls below a minimum threshold value. Below this threshold the QoS is deemed unacceptable in terms of BER and the associated probability of outage in service.

2.2Energy Efficiency

Although some guaranteed level of QoS is a clear necessity, for service provision issues such as energy consumption, battery life and size are proving to be important factors when it comes to increasing the uptake of new WSN systems. Placing an upper bound on power consumption in order to maximise operational longevity is therefore also a requirement. This poses a difficult challenge as many factors can contribute to energy consumption for any given WSN deployment. However one suggestion was made in (Otto et al., 2006) where empirical evidence attributed 95% of the overall energy consumed by a wireless sensor node to communication. To narrow the focus further it was highlighted in (Zurita Ares et al., 2007) that 70% of the energy consumed by widely available WSN platforms is as a result of data transmission alone. It therefore stands to reason that minimising the time spent transmitting or optimising transceiver output power can aid greatly in energy efficiency.

2.3Network Coverage Area

In (Mobihealthnews, 2009) it was suggested that wireless networks in healthcare applications need to perform to “mission critical perfection”, where the end user must have no concerns over network coverage. It was highlighted that real service should not be “homebound” in nature but rather some level of ambulatory motion must be provided, without any technical concerns about information loss being a factor. As WSN technology is for the most part a low range solution, some design consideration must be given to provision for the need to extend network coverage area. A multi-hop hierarchy is a clear

solution to this problem, however when mobility is considered the need for handoff is introduced as a by-product. Whether it is between access points within a network or between networks, handoff must appear seamless to the user and the service must where possible remain uninterrupted.

2.4 Hardware Constraints

Practical limitations are a feature of any WSN. Without exception each wireless technology is bandwidth limited and is therefore prone to congestion under heavy workloads. However empirical evidence would suggest that hardware limitations will inevitably become a factor prior to the impingement of bandwidth constraints. For instance, the IEEE 802.15.4 standard specified at 2.4 GHz supports a bandwidth of 250 kbps (IEEE 802.15.4 Standard, 2006). However, the state-of-the-art 802.15.4 compliant Tmote Sky platform can achieve only 125 kbps maximum upload and 150 kbps download over the air, as a result of microcontroller process saturation (Polastre, 2005).

Other practical hardware constraints must also be considered. Transceiver output power limitations are an omnipresent feature of the WSN device. This nonlinearity can severely degrade network performance when encountered and can potentially destabilize the system entirely. Quantisation is also invariably present in a wireless communications system. Generally, a radio transceiver has a discrete number of output power levels and switching between these levels introduces unwanted quantisation noise into the system. This undesirable additional noise signal can impact negatively on communications quality. While each of these constraints is unavoidable, in practice, it is vital that their negative impact on the communication quality should be limited in an efficient manner.

3. A Solution in Systems Science

This work proposes a number of novel systems science based solutions tackling the challenges outlined above. The wireless architecture illustrated in Fig. 1 is envisaged. The IEEE 802.15.4 standard is referred to throughout as a benchmark technology, although each of the proposed methodologies presented is extendable to the general case.

(4)

engineer is therefore presented with many challenges when designing an effective deployment.

2. Wireless Sensor Network Challenges

There are numerous challenges that must be addressed when designing a WSN. There follows a brief look at a number of problems, general in the wireless context, to which systems science can provide a useful solution.

2.1Reliable Quality of Service

In a survey carried out amongst possible users of industrial wireless technology (IMS Research, 2006), 43% of the surveyed suggested that communications reliability was a major barrier to the uptake of wireless solutions in industry. The provision for Quality of Service (QoS) is therefore a key requirement if any form of WSN market penetration is to be generated. QoS has a number of different associated meanings (Goldsmith, 2006; Rappaport, 2002). In this work, QoS is taken, where specified, to imply one or both of the following

1. QoS implies that the transmitted signal will exhibit certain minimum signal strength at the receiver. This in turn will guarantee pre-specified levels of Bit Error Rate (BER) and improve demodulation at the point of access.

2. System connectivity must be ensured under the assumption that the communication link will be severed if some reliable measurable link quality metric falls below a minimum threshold value. Below this threshold the QoS is deemed unacceptable in terms of BER and the associated probability of outage in service.

2.2Energy Efficiency

Although some guaranteed level of QoS is a clear necessity, for service provision issues such as energy consumption, battery life and size are proving to be important factors when it comes to increasing the uptake of new WSN systems. Placing an upper bound on power consumption in order to maximise operational longevity is therefore also a requirement. This poses a difficult challenge as many factors can contribute to energy consumption for any given WSN deployment. However one suggestion was made in (Otto et al., 2006) where empirical evidence attributed 95% of the overall energy consumed by a wireless sensor node to communication. To narrow the focus further it was highlighted in (Zurita Ares et al., 2007) that 70% of the energy consumed by widely available WSN platforms is as a result of data transmission alone. It therefore stands to reason that minimising the time spent transmitting or optimising transceiver output power can aid greatly in energy efficiency.

2.3Network Coverage Area

In (Mobihealthnews, 2009) it was suggested that wireless networks in healthcare applications need to perform to “mission critical perfection”, where the end user must have no concerns over network coverage. It was highlighted that real service should not be “homebound” in nature but rather some level of ambulatory motion must be provided, without any technical concerns about information loss being a factor. As WSN technology is for the most part a low range solution, some design consideration must be given to provision for the need to extend network coverage area. A multi-hop hierarchy is a clear

solution to this problem, however when mobility is considered the need for handoff is introduced as a by-product. Whether it is between access points within a network or between networks, handoff must appear seamless to the user and the service must where possible remain uninterrupted.

2.4 Hardware Constraints

Practical limitations are a feature of any WSN. Without exception each wireless technology is bandwidth limited and is therefore prone to congestion under heavy workloads. However empirical evidence would suggest that hardware limitations will inevitably become a factor prior to the impingement of bandwidth constraints. For instance, the IEEE 802.15.4 standard specified at 2.4 GHz supports a bandwidth of 250 kbps (IEEE 802.15.4 Standard, 2006). However, the state-of-the-art 802.15.4 compliant Tmote Sky platform can achieve only 125 kbps maximum upload and 150 kbps download over the air, as a result of microcontroller process saturation (Polastre, 2005).

Other practical hardware constraints must also be considered. Transceiver output power limitations are an omnipresent feature of the WSN device. This nonlinearity can severely degrade network performance when encountered and can potentially destabilize the system entirely. Quantisation is also invariably present in a wireless communications system. Generally, a radio transceiver has a discrete number of output power levels and switching between these levels introduces unwanted quantisation noise into the system. This undesirable additional noise signal can impact negatively on communications quality. While each of these constraints is unavoidable, in practice, it is vital that their negative impact on the communication quality should be limited in an efficient manner.

3. A Solution in Systems Science

This work proposes a number of novel systems science based solutions tackling the challenges outlined above. The wireless architecture illustrated in Fig. 1 is envisaged. The IEEE 802.15.4 standard is referred to throughout as a benchmark technology, although each of the proposed methodologies presented is extendable to the general case.

(5)

A layered approach is adopted where the goal is to exploit fully the hardware and software capabilities of the employed technology, to improve the overall service to the user. This is achieved by firstly providing suitable hardware abstractions completely exposing the functionality of the WSN hardware devices. This functionality is presented to the upper layers in the form of simple function calls. Systems science based middleware solutions are then proposed utilizing the hardware abstraction. In this regard, robust dynamic power and handoff schemes are designed and implemented on a fully compliant 802.15.4 benchmark testbed. Quantifiable improvements are reported in terms of QoS, energy efficiency and network coverage. The emphasis is placed on modularity where code reuse is encouraged sparing valuable network resources.

3.1 Closed Loop Feedback Control over Wireless Networks

The goal of any closed loop feedback system is to firstly measure a feedback metric employing a sensor of some type to do so. This measurement is compared with a predefined reference value. A subsequent control command update is generated using the difference between these two signals as an input to the controller and the plant actuators are adjusted accordingly. In traditional feedback control systems, the feedback loop and the connection between the controller and the plant are fixed or wired in nature as in Fig. 2.

Closed loop control over wireless networks differs in that, the feedback loop and/or the control command update link are/is wireless in nature. This places an additional constraint on the system as the wireless radio channel is typically affected by exogenous, uncertain factors that must necessarily have an adverse impact on system performance. This inevitably makes the controller design and implementation more difficult. However, with a more detailed understanding of wireless channel behaviour, robust control design techniques can be extended to the WSN case and can in turn improve overall operating efficiency.

Fig. 2. The Closed Loop Feedback Structure

4. A Canonical Closed-loop Distributed Power Control Structure for WSNs

The goal of this scheme is to dynamically adjust device transmitter power, from a finite list of available levels, in a distributed manner so that the power consumption is minimized while also maintaining sufficient transmission quality. The received signal strength indicator (RSSI) is selected as the dynamic variable to manage this objective. In the past, it has been suggested that RSSI was a less than ideal metric for control. This claim however was based on experimentation with early platforms that used radios, e.g. the Texas Instruments CC1000, where hardware miscalibration or drift was often a problem. However, in recent times the use of RSSI has undergone something of a renaissance, with newer radios

such as the 802.15.4 compliant TI CC2420 exhibiting highly stable performance. For example, in (Srinivasan and Levis, 2006), RSSI was proven to exhibit quite insignificant time variability as long as it stayed above an a priori defined threshold level. Recent empirical evidence would also suggest this to be the case (Alavi et al., 2008; Walsh et al., 2008; Walsh et al., 2009).

Fig. 3. Block diagram of the WSN Closed Loop Distributed Power Control structure based on RSSI measurement.

The proposed canonical closed loop WSN power control structure is illustrated in Fig. 3. A decentralized scheme is envisaged where the RSSI r(k) is measured at the access point or coordinator and compared with a target value rt. The difference or error e(k) is then fed into the controller C(z), a number of realisations for which are presented in subsequent sections. The controller outputs a command update which in turn is passed to the plant G(z). The plant outputs a power update which is limited by the inherent quantisation and saturation constraints. The resultant command pm(k) is transmitted to the mobile node where the new

output power value is applied. In this scheme



1 and



2 represent downlink and uplink transmission delays respectively.

The objective therefore is to design C(z) such that rt is efficiently tracked, thusly guaranteeing QoS while minimising power consumption. C(z) must be robust to time varying stochastic channel uncertainties and interference which are modelled in this paradigm as an output disturbance. This simplifies controller design to some extent, as when the worst case interference and uncertainty scenarios are considered in the synthesis routine, exact information in relation to these difficult to quantify metrics is not required in realtime (Alavi et al., 2008). The hardware constraints must also be addressed in a manner so as to limit their impact on system performance. It is also worthwhile noting that almost all computational work is carried out at the access point. This allows for star topological deployments where the mobile nodes may be Reduced Functional Devices (RFDs).

4.1 Relating Received Signal Strength to Signal-to-Interferenceplus Noise Ratio

Working under the assumption that noise is correctly filtered at the receiver, (Zurita Ares et al., 2007) introduced a method to directly estimate the signal to noise plus interference ratio (SINR) using RSSI measurements. This approach denotes RSSI as,

30 ) ( ) ( ) ( ) (k p k g k I k   r (1)

(6)

A layered approach is adopted where the goal is to exploit fully the hardware and software capabilities of the employed technology, to improve the overall service to the user. This is achieved by firstly providing suitable hardware abstractions completely exposing the functionality of the WSN hardware devices. This functionality is presented to the upper layers in the form of simple function calls. Systems science based middleware solutions are then proposed utilizing the hardware abstraction. In this regard, robust dynamic power and handoff schemes are designed and implemented on a fully compliant 802.15.4 benchmark testbed. Quantifiable improvements are reported in terms of QoS, energy efficiency and network coverage. The emphasis is placed on modularity where code reuse is encouraged sparing valuable network resources.

3.1 Closed Loop Feedback Control over Wireless Networks

The goal of any closed loop feedback system is to firstly measure a feedback metric employing a sensor of some type to do so. This measurement is compared with a predefined reference value. A subsequent control command update is generated using the difference between these two signals as an input to the controller and the plant actuators are adjusted accordingly. In traditional feedback control systems, the feedback loop and the connection between the controller and the plant are fixed or wired in nature as in Fig. 2.

Closed loop control over wireless networks differs in that, the feedback loop and/or the control command update link are/is wireless in nature. This places an additional constraint on the system as the wireless radio channel is typically affected by exogenous, uncertain factors that must necessarily have an adverse impact on system performance. This inevitably makes the controller design and implementation more difficult. However, with a more detailed understanding of wireless channel behaviour, robust control design techniques can be extended to the WSN case and can in turn improve overall operating efficiency.

Fig. 2. The Closed Loop Feedback Structure

4. A Canonical Closed-loop Distributed Power Control Structure for WSNs

The goal of this scheme is to dynamically adjust device transmitter power, from a finite list of available levels, in a distributed manner so that the power consumption is minimized while also maintaining sufficient transmission quality. The received signal strength indicator (RSSI) is selected as the dynamic variable to manage this objective. In the past, it has been suggested that RSSI was a less than ideal metric for control. This claim however was based on experimentation with early platforms that used radios, e.g. the Texas Instruments CC1000, where hardware miscalibration or drift was often a problem. However, in recent times the use of RSSI has undergone something of a renaissance, with newer radios

such as the 802.15.4 compliant TI CC2420 exhibiting highly stable performance. For example, in (Srinivasan and Levis, 2006), RSSI was proven to exhibit quite insignificant time variability as long as it stayed above an a priori defined threshold level. Recent empirical evidence would also suggest this to be the case (Alavi et al., 2008; Walsh et al., 2008; Walsh et al., 2009).

Fig. 3. Block diagram of the WSN Closed Loop Distributed Power Control structure based on RSSI measurement.

The proposed canonical closed loop WSN power control structure is illustrated in Fig. 3. A decentralized scheme is envisaged where the RSSI r(k) is measured at the access point or coordinator and compared with a target value rt. The difference or error e(k) is then fed into the controller C(z), a number of realisations for which are presented in subsequent sections. The controller outputs a command update which in turn is passed to the plant G(z). The plant outputs a power update which is limited by the inherent quantisation and saturation constraints. The resultant command pm(k) is transmitted to the mobile node where the new

output power value is applied. In this scheme



1 and



2 represent downlink and uplink transmission delays respectively.

The objective therefore is to design C(z) such that rt is efficiently tracked, thusly guaranteeing QoS while minimising power consumption. C(z) must be robust to time varying stochastic channel uncertainties and interference which are modelled in this paradigm as an output disturbance. This simplifies controller design to some extent, as when the worst case interference and uncertainty scenarios are considered in the synthesis routine, exact information in relation to these difficult to quantify metrics is not required in realtime (Alavi et al., 2008). The hardware constraints must also be addressed in a manner so as to limit their impact on system performance. It is also worthwhile noting that almost all computational work is carried out at the access point. This allows for star topological deployments where the mobile nodes may be Reduced Functional Devices (RFDs).

4.1 Relating Received Signal Strength to Signal-to-Interferenceplus Noise Ratio

Working under the assumption that noise is correctly filtered at the receiver, (Zurita Ares et al., 2007) introduced a method to directly estimate the signal to noise plus interference ratio (SINR) using RSSI measurements. This approach denotes RSSI as,

30 ) ( ) ( ) ( ) (k p k g k I k   r (1)

(7)

where r(k) is the RSSI value, p(k) and g(k)are output power and attenuation respectively and I(k) contains path-loss, shadowing, fading, interference and noise. The addition of the scalar term 30 accounts for the conversion from dBm to dB and  is the measurement offset determined empirically to be 45 dB. From (Zurita Ares et al., 2007) the SINR (k), in terms of RSSI can be described as,

30 ) ( ) (    k r k (2) This relationship is useful for a number of reasons. Firstly expressing RSSI in terms of SINR which in turn can be related to PER, is a suitable means of guaranteeing pre-specified levels of QoS in the closed loop system. To expand a target or reference RSSI value can be selected and related directly to PER, as outlined in the 802.15.4 standard (IEEE 802.15.4 Standard, 2006). The bit error rate (BER) for the 802.15.4 standard operating at a frequency of 2.4GHz is given by,



              16 2 ) 1 1 ( 20 16 1 16 1 15 8 k k SINR k _e k BER (3) and given the average packet length for this standard is 22 bytes, the PER can be obtained from,

PL

BER

PER1(1 ) (4) where PL is packet length including the header and payload. PER is more useful here given the transceiver used to practically implement the proposed methodology, is a wideband transceiver, transmitting and receiving data in packet rather then bit format. Establishing a relationship between RSSI, SINR, BER and subsequently PER can therefore help to pre-specify levels of system performance. The relationship can also be used for comparative purposes, given control algorithms employing SINR, as a feedback metric can be directly applied to the WSN closed loop power control structure in Fig. 3. This is a useful tool in evaluating the performance of the proposed power control solution that follows.

4.2Practical Hardware Limitations

Practical hardware limitations are a feature of any hardware platform and can result in severe performance degradation if not handled correctly. Addressing these constraints in parallel with improving reliability and power awareness is therefore a worthwhile endeavour.

Fig. 4. Transceiver Output Power Saturation Nonlinearity

There is a maximum and minimum power at which any transceiver can transmit. These limits introduce a nonlinear saturation element to the system. The saturation nonlinearity

sat(.) is illustrated in Fig. 4 and can be represented by equation (5).

(5) Without exception, there are also constraints placed on the system by the discrete nature of a transceiver's power levels. The impact switching between each discrete power level can adversely affect system performance as quantisation error is introduced. This additional input is normally modelled as noise. Generally, this signal is small in magnitude when compared with the channel variation associated with propagation effects; however it should be considered in any effective control design solution. The quantization and saturation nonlinearities are illustrated in Fig. 5.

Fig. 5. Transceiver Output Quantisation Nonlinearity

Fig. 6. The Anti-Windup approach as it applies to the Wireless Sensor Network Power Control Problem

(8)

where r(k) is the RSSI value, p(k) and g(k)are output power and attenuation respectively and I(k) contains path-loss, shadowing, fading, interference and noise. The addition of the scalar term 30 accounts for the conversion from dBm to dB and  is the measurement offset determined empirically to be 45 dB. From (Zurita Ares et al., 2007) the SINR (k), in terms of RSSI can be described as,

30 ) ( ) (    k r k (2) This relationship is useful for a number of reasons. Firstly expressing RSSI in terms of SINR which in turn can be related to PER, is a suitable means of guaranteeing pre-specified levels of QoS in the closed loop system. To expand a target or reference RSSI value can be selected and related directly to PER, as outlined in the 802.15.4 standard (IEEE 802.15.4 Standard, 2006). The bit error rate (BER) for the 802.15.4 standard operating at a frequency of 2.4GHz is given by,



              16 2 ) 1 1 ( 20 16 1 16 1 15 8 k k SINR k _e k BER (3) and given the average packet length for this standard is 22 bytes, the PER can be obtained from,

PL

BER

PER1(1 ) (4) where PL is packet length including the header and payload. PER is more useful here given the transceiver used to practically implement the proposed methodology, is a wideband transceiver, transmitting and receiving data in packet rather then bit format. Establishing a relationship between RSSI, SINR, BER and subsequently PER can therefore help to pre-specify levels of system performance. The relationship can also be used for comparative purposes, given control algorithms employing SINR, as a feedback metric can be directly applied to the WSN closed loop power control structure in Fig. 3. This is a useful tool in evaluating the performance of the proposed power control solution that follows.

4.2Practical Hardware Limitations

Practical hardware limitations are a feature of any hardware platform and can result in severe performance degradation if not handled correctly. Addressing these constraints in parallel with improving reliability and power awareness is therefore a worthwhile endeavour.

Fig. 4. Transceiver Output Power Saturation Nonlinearity

There is a maximum and minimum power at which any transceiver can transmit. These limits introduce a nonlinear saturation element to the system. The saturation nonlinearity

sat(.) is illustrated in Fig. 4 and can be represented by equation (5).

(5) Without exception, there are also constraints placed on the system by the discrete nature of a transceiver's power levels. The impact switching between each discrete power level can adversely affect system performance as quantisation error is introduced. This additional input is normally modelled as noise. Generally, this signal is small in magnitude when compared with the channel variation associated with propagation effects; however it should be considered in any effective control design solution. The quantization and saturation nonlinearities are illustrated in Fig. 5.

Fig. 5. Transceiver Output Quantisation Nonlinearity

Fig. 6. The Anti-Windup approach as it applies to the Wireless Sensor Network Power Control Problem

(9)

5. An Anti-Windup solution to Robust Power Control

Consider a WSN implementing power control in a distribute manner and subject to practical hardware limitations as per any deployment of this nature. The focus here is placed on assessing the effect that the limited power transmission capabilities of a typical mobile node, within a practical sensor network, will have on performance. These natural hardware constraints will impose saturation type limits that will obviously severely degrade network performance. In this chapter, a two step Anti-Windup (AW) design procedure is introduced to tackle this problem. The first step is to design a linear controller, ignoring the inherent nonlinear constraints that are placed on the system that uses a Quantitative Feedback Theory (QFT) approach to provide both robust stability and nominal performance in the linear region of operation. A feature of this first step is that it naturally bounds the time domain response of the system for a particular power level and provides a basis for assessing how a change in the quantisation noise caused by power level selection will affect performance. The second step, shown in Fig. 6, incorporates recent advances in AW theory to minimize performance degradation in the face of actuator constraints.

5.1 The Simplified System Model

A systems science representation of a single access point communicating to a single mobile node is illustrated in Fig. 7. The system has reference input r(k) (reference RSSI), the value for which is determined using (2), (3) and (4) above, guaranteeing a predefined PER. q(k) is quantization noise introduced as a result of switching between discrete power levels. The controller K(z) has controller output u(k) and takes the form K(z) = [K1(z) K2(z)], a standard

two degree of freedom structure.

Fig. 7. Wireless System Model with saturation block at the output.

The plant G(z) is represented by G(z) = [G1(z) G2(z)], where G1(z) and G2(z) are the

disturbance feedforward and feedback parts of G(z) respectively. Given no structured disturbance model is available in the form of a transfer function, G1(z) is taken to be G1 = I,

where I is the identity matrix. The approach adopted regard to modelling G2(z) is similar to

that suggested by (Gunnarsson et al., 1999) where the plant model for the WSN device is no longer represented by an integrator. However, rather than replace the plant model with a direct feedthrough term, (i.e., for a device G and power command update pi, the plant

output is G(pi) = pi), the plant is herein modelled as a low pass filter possessed of sufficient

available bandwidth to be robust to a particular level of quantizationnoise. G2(z) is therefore

selected as, 9 . 0 1 . 1 1 ) ( 2 z  _z_ G (6)

G2(z) outputs a power level update p(k), which in turn is transmitted to the mobile node. The

mobile node transmitter has inherent upper and lower bounds on hardware transmission power output, represented in Fig. 7 by the saturation block, the output for which is saturated output power or pm(k). H represents the hardware switch in the mobile node’s

transceiver and is taken here to be the identity matrix or H = I. d(k) is a disturbance to the system and comprises of channel attenuation, interference and noise.

5.2 Mapping the Saturation Function

For this scenario, a problem presents itself in that the saturation constraint is located at the output of the system and while there have been some advances in control design theory to deal with this type of output constraint for instance (Grandhi et al., 1995; Andersin et al., 1998), there is a vast literature covering the treatment of linear systems subject to input saturation constraints, see (Bernstein and Michel, 1995) and references therein. A solution therefore lies in the mapping of the output saturation constraint to the input of the plant or the output of the controller. The saturation function is defined as,

)) ( ( ) (k sat p k p_m  (7) where sat(p(k))sign(p(k))min{|p(k)|,p_m(k)} and p_m(k) is the output power saturation limit. Note the sat(.) function in (6), belongs to sector [0, 1] and is assumed locally Lipschitz. The following set is defined,

)] ( ), ( [p_m k p_m k   (8) where sat(p(k))p(k),p(k) . This is the set in which the saturation behaves linearly i.e. if there is no saturation present p(k)p_m(k)] and the nominal closed loop system conditions are exhibited. Fig. 8 portrays the system with the saturation block mapped from the output of the system to the input where um(k) is the input to the plant. To represent the mapped

saturation function we define the new set,

] ) ( , ) ( [ 2 2 G m G m h k p h k p    (9) where h is the gain of the transfer function G_G₂ 2. Recent advances in the antiwindup literature can now be applied to the problem at hand, ensuring minimal performance degradation during saturation and speedy recovery following saturation.

Fig. 8. Wireless System Model with saturation block mapped from the output to the input of the system.

(10)

5. An Anti-Windup solution to Robust Power Control

Consider a WSN implementing power control in a distribute manner and subject to practical hardware limitations as per any deployment of this nature. The focus here is placed on assessing the effect that the limited power transmission capabilities of a typical mobile node, within a practical sensor network, will have on performance. These natural hardware constraints will impose saturation type limits that will obviously severely degrade network performance. In this chapter, a two step Anti-Windup (AW) design procedure is introduced to tackle this problem. The first step is to design a linear controller, ignoring the inherent nonlinear constraints that are placed on the system that uses a Quantitative Feedback Theory (QFT) approach to provide both robust stability and nominal performance in the linear region of operation. A feature of this first step is that it naturally bounds the time domain response of the system for a particular power level and provides a basis for assessing how a change in the quantisation noise caused by power level selection will affect performance. The second step, shown in Fig. 6, incorporates recent advances in AW theory to minimize performance degradation in the face of actuator constraints.

5.1 The Simplified System Model

A systems science representation of a single access point communicating to a single mobile node is illustrated in Fig. 7. The system has reference input r(k) (reference RSSI), the value for which is determined using (2), (3) and (4) above, guaranteeing a predefined PER. q(k) is quantization noise introduced as a result of switching between discrete power levels. The controller K(z) has controller output u(k) and takes the form K(z) = [K1(z) K2(z)], a standard

two degree of freedom structure.

Fig. 7. Wireless System Model with saturation block at the output.

The plant G(z) is represented by G(z) = [G1(z) G2(z)], where G1(z) and G2(z) are the

disturbance feedforward and feedback parts of G(z) respectively. Given no structured disturbance model is available in the form of a transfer function, G1(z) is taken to be G1 = I,

where I is the identity matrix. The approach adopted regard to modelling G2(z) is similar to

that suggested by (Gunnarsson et al., 1999) where the plant model for the WSN device is no longer represented by an integrator. However, rather than replace the plant model with a direct feedthrough term, (i.e., for a device G and power command update pi, the plant

output is G(pi) = pi), the plant is herein modelled as a low pass filter possessed of sufficient

available bandwidth to be robust to a particular level of quantizationnoise. G2(z) is therefore

selected as, 9 . 0 1 . 1 1 ) ( 2 z  _z_ G (6)

G2(z) outputs a power level update p(k), which in turn is transmitted to the mobile node. The

mobile node transmitter has inherent upper and lower bounds on hardware transmission power output, represented in Fig. 7 by the saturation block, the output for which is saturated output power or pm(k). H represents the hardware switch in the mobile node’s

transceiver and is taken here to be the identity matrix or H = I. d(k) is a disturbance to the system and comprises of channel attenuation, interference and noise.

5.2 Mapping the Saturation Function

For this scenario, a problem presents itself in that the saturation constraint is located at the output of the system and while there have been some advances in control design theory to deal with this type of output constraint for instance (Grandhi et al., 1995; Andersin et al., 1998), there is a vast literature covering the treatment of linear systems subject to input saturation constraints, see (Bernstein and Michel, 1995) and references therein. A solution therefore lies in the mapping of the output saturation constraint to the input of the plant or the output of the controller. The saturation function is defined as,

)) ( ( ) (k sat p k p_m  (7) where sat(p(k))sign(p(k))min{|p(k)|,p_m(k)} and p_m(k) is the output power saturation limit. Note the sat(.) function in (6), belongs to sector [0, 1] and is assumed locally Lipschitz. The following set is defined,

)] ( ), ( [p_m k p_m k   (8) where sat(p(k))p(k),p(k) . This is the set in which the saturation behaves linearly i.e. if there is no saturation present p(k)p_m(k)] and the nominal closed loop system conditions are exhibited. Fig. 8 portrays the system with the saturation block mapped from the output of the system to the input where um(k) is the input to the plant. To represent the mapped

saturation function we define the new set,

] ) ( , ) ( [ 2 2 G m G m h k p h k p    (9) where h is the gain of the transfer function G_G₂ 2. Recent advances in the antiwindup literature can now be applied to the problem at hand, ensuring minimal performance degradation during saturation and speedy recovery following saturation.

Fig. 8. Wireless System Model with saturation block mapped from the output to the input of the system.

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5.3 Robust Linear Power Tracking Controller Design

Quantitative feedback theory (QFT) provides an intuitively appealing means of guaranteeing both robust stability and performance and is essentially a Two-Degree-of-Freedom (2DOF) frequency domain technique, as illustrated in Fig. 8. The scheme achieves client-specified levels of desired performance over a region of parametric plant uncertainty, determined a priori by the engineer. The methodology requires that the desired time-domain responses are translated into frequency time-domain tolerances, which in turn lead to design bounds in the loop function on the Nichols chart. In a QFT design, the responsibility of the feedback compensator, K2(z), is to focus primarily on attenuating the undesirable

effects of uncertainty, disturbance and noise. Having arrived at an appropriate K2(z), a

pre-filter K1(z), is then designed so as to shift the closed-loop response to the desired tracking

region, again specified a priori by the engineer. The approach requires that the designer select a set of desired specifications in relation to the magnitude of the frequency response of the closed-loop system, thusly achieving robust stability and performance. The design procedure in its entirety is omitted here due to space constraints, however the interested reader is directed to (Horowitz, 2001) and references therein. Using this technique, K2(z) was

found to be, 7103 . 0 7103 . 0 6622 . 0 ) ( 2 z  z_z_ K (10) guaranteeing a phase and gain margin equal to 50o _{and 1.44, respectively. The closed-loop} transfer function is shaped using K1(z) ensuring the system achieves steady state around the

target value of 5t_ss 25(s) and a damping factor of  = 0.5 is selected to reduce outage probability at the outset of communication. The resultant K1(z) is,

4127 . 0 4127 . 1 ) ( 1 z  _z_ z K (11)

5.4 Weston Postlethwaite Anti-Windup Synthesis

Consider the generic AW configuration shown in Fig. 9. As illustrated above the plant takes the form G(z) = [G1(z) G2(z)], the linear controller is represented by K(z) = [K1(z) K2(z)], and

= [1(z) 2(z)] is the AW controller becoming active only when saturation occurs. Given the

difficulty in analyzing the stability and performance of this system we now adopt a framework first introduced in (Weston and Postlewaite, 2000) for the problem at hand. This approach reduces to a linear time invariant Anti-Windup scheme that is optimized in terms of one transfer function M(z) shown in Fig.10. It was shown by (Weston and Postlewaite, 2000) that the performance degradation experienced by the system during saturation is directly related to the mapping T:u_liny_d. This may not be clear at first glance, however if one looks at the equivalent representation of the system illustrated in Fig.11 and derived in (Weston and Postlewaite, 2000), it can be seen that the decoupled system is divided into three sections: the nominal linear system, the disturbance filter and the nonlinear loop. Note that from Fig. 11, M - I is considered for the stability of T and G2M determines the system

recovery after saturation. This decoupled representation clearly illustrates how this

mapping can be utilized as a performance measure for the AW controller. To quantify this an AW controller is selected such that the l2-gain, T _,i₂, of the operator T,

2 2 0 2 , 2 sup lin d l u i _u y T lin   (12) where the l2 norm x of a discrete signal x(h),(h=0,1,2,3,….) is, ₂



   0 2 2 ( ) h h x x (13)

Fig. 9. A generic anti-windup scenario.

Fig. 10. Weston Postlethwaite Anti-Windup conditioning technique.

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5.3 Robust Linear Power Tracking Controller Design

Quantitative feedback theory (QFT) provides an intuitively appealing means of guaranteeing both robust stability and performance and is essentially a Two-Degree-of-Freedom (2DOF) frequency domain technique, as illustrated in Fig. 8. The scheme achieves client-specified levels of desired performance over a region of parametric plant uncertainty, determined a priori by the engineer. The methodology requires that the desired time-domain responses are translated into frequency time-domain tolerances, which in turn lead to design bounds in the loop function on the Nichols chart. In a QFT design, the responsibility of the feedback compensator, K2(z), is to focus primarily on attenuating the undesirable

effects of uncertainty, disturbance and noise. Having arrived at an appropriate K2(z), a

pre-filter K1(z), is then designed so as to shift the closed-loop response to the desired tracking

region, again specified a priori by the engineer. The approach requires that the designer select a set of desired specifications in relation to the magnitude of the frequency response of the closed-loop system, thusly achieving robust stability and performance. The design procedure in its entirety is omitted here due to space constraints, however the interested reader is directed to (Horowitz, 2001) and references therein. Using this technique, K2(z) was

found to be, 7103 . 0 7103 . 0 6622 . 0 ) ( 2 z  z_z_ K (10) guaranteeing a phase and gain margin equal to 50o _{and 1.44, respectively. The closed-loop} transfer function is shaped using K1(z) ensuring the system achieves steady state around the

target value of 5t_ss 25(s) and a damping factor of  = 0.5 is selected to reduce outage probability at the outset of communication. The resultant K1(z) is,

4127 . 0 4127 . 1 ) ( 1 z  _z_ z K (11)

5.4 Weston Postlethwaite Anti-Windup Synthesis

Consider the generic AW configuration shown in Fig. 9. As illustrated above the plant takes the form G(z) = [G1(z) G2(z)], the linear controller is represented by K(z) = [K1(z) K2(z)], and

= [1(z) 2(z)] is the AW controller becoming active only when saturation occurs. Given the

difficulty in analyzing the stability and performance of this system we now adopt a framework first introduced in (Weston and Postlewaite, 2000) for the problem at hand. This approach reduces to a linear time invariant Anti-Windup scheme that is optimized in terms of one transfer function M(z) shown in Fig.10. It was shown by (Weston and Postlewaite, 2000) that the performance degradation experienced by the system during saturation is directly related to the mapping T:u_liny_d. This may not be clear at first glance, however if one looks at the equivalent representation of the system illustrated in Fig.11 and derived in (Weston and Postlewaite, 2000), it can be seen that the decoupled system is divided into three sections: the nominal linear system, the disturbance filter and the nonlinear loop. Note that from Fig. 11, M - I is considered for the stability of T and G2M determines the system

recovery after saturation. This decoupled representation clearly illustrates how this

mapping can be utilized as a performance measure for the AW controller. To quantify this an AW controller is selected such that the l2-gain, T _,i₂, of the operator T,

2 2 0 2 , 2 sup lin d l u i _u y T lin   (12) where the l2 norm x of a discrete signal x(h),(h=0,1,2,3,….) is, ₂



   0 2 2 ( ) h h x x (13)

Fig. 9. A generic anti-windup scenario.

Fig. 10. Weston Postlethwaite Anti-Windup conditioning technique.

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5.5 Static anti-windup synthesis

Static AW has an advantage in that it can be implemented at a much lower computational cost and adds no additional states to the closed loop system. Full order AW synthesis or AW with order equal to the plant will often lead to less response deterioration during saturation, however significant computation is required. This is often unacceptable, especially in systems that are of higher order and where additional states are undesirable. For this reason, it is common practice that most windup problems are suppressed using static compensators, see for example (Hanus et al., 1987). Using the aforementioned conditioning technique via

M(z), outlined in (Turner and Postlethwaite 2004), from Fig. 9 is given by,

uˆ uˆ 2 1 2 1                    (14) where u is derived from Figs. 9 and 10, respectively as,

u K y K r K u u I M G K I y K r K u ˆ ) ( ˆ ] ) [( 1 2 2 2 1 2 2 2 1            (15) Thus, M(z) can be written as,

M(IK₂G₂)1(K₂₂₁I) (16) The goal of the static AW approach is therefore to ensure that extra modes do not appear in the system. Since this will inevitably be the case, it must be ensured that minimal realizations of the controller and plant are used (Turner and Postlethwaite 2004). A state space realization can then be formed,

_                                         u x D D C D D C B B A y u x z N I z M d d _ˆ ) ( ) ( 2 02 2 1 01 1 0  (17) where = [1(z) 2(z)] is a static matrix and x , A , B₀, B , C , ₁ D₀₁, D , ₁ C , ₂ D and ₀₂ D ₂

are minimal realizations given in Appendix A. A solution is obtained for the Linear Matrix Inequality (LMI) in (18) with Q>0,U =diag(v1, . . .,vc)>0, L   (c+n)×n (where c=n), and the

minimized l2 gain T _,i₂  (where  is the l2 gain bound on T). In this instance,  is given by  =L−1_{using which, the}

0 0 0 0 ' ' ' ' ' ' 0 ' ' 2 01 0 2 1 1                                      I I Q D L UD I B L UB X C Q A Q C Q Q   (18)

where X2UD₀₁UD₁LUD'₀₁L'D'₁

.

Such an l2 design ensures that during saturation

closed-loop performance is achieved by staying close to the nominal design while the time

spent in saturation is also jointly minimized. Applying this synthesis routine to our plant given by (6) and linear controller (18), the resultant controller is =[−0.2049 0.6377]’ obtained using the LMI toolbox in Matlab.

6. An Anti-Windup approach to Power Aware Seamless Handoff

A major WSN challenge lies in maximizing network coverage area. Given that many of the “off-the-shelf" sensor node platforms operate using low power wireless sensor technologies, transmission range is extremely limited, especially in the indoor environment. A multihop or mesh network topology is often proposed in order to extend coverage area necessitating the introduction of a handoff protocol that is power aware. Fig. 12 illustrates the type of scenario that is envisaged whereby subject X is being monitored and is wearing (perhaps a number of) wireless biometric devices. Initially X is in communication with base station BS1. When X moves to an adjoining area in an ambulatory fashion, data must at some point be transmitted via BS2 rather than BS1. It is crucial that the QoS and energy efficient properties of the network be retained in such a scenario. This chapter proposes a Bumpless Transfer (BT) scheme to optimize this naturally nonlinear switching process. In any BT scheme, the global controller oversees multiple local loop devices that are designed to ensure the network is both power and QoS aware. Depending on certain performance requirements, a sequence of switches is necessary between each controller. In essence, one controller will be operational or “on-line" while the other candidate controller(s) must be deemed “off-line" at any instant. Clearly, it is necessary to be able to switch between these controllers (located at adjacent base stations or access points) in a stable fashion. Sufficient conditions must therefore be established to ensure that the induced transient signals are bounded, thereby satisfying network stability requirements. To achieve this smoothly, the gap between the off and on-line control signals must be bounded so that the control signal driving the plant cannot induce instability.

Fig. 12. The ambient healthcare environment. Power control for X is initially handled by BS1. Subject X then moves in an ambulatory fashion and handoff occurs between BS1 and BS2. Data is now multi-hopped via BS2 to BS1 and BS2 handles power control for X. Hence, power controller handoff has occurred between BS1 and BS2.

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